MinT - Best Known (48, 48+47, s)-Nets in Base 4

Best Known (48, 48+47, s)-Nets in Base 4

(48, 48+47, 60)-Net over F₄ — Constructive and digital

Digital (48, 95, 60)-net over F₄, using

(u,Â u+v)-construction [i] based on
1. digital (10, 33, 27)-net over F₄, using
  - net from sequence [i] based on digital (10, 26)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 10 and N(F) ≥ 27, using
      - an explicitly constructive algebraic function field [i]
2. digital (15, 62, 33)-net over F₄, using
  - net from sequence [i] based on digital (15, 32)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 15 and N(F) ≥ 33, using
      - an explicitly constructive algebraic function field [i]

(48, 48+47, 65)-Net in Base 4 — Constructive

(48, 95, 65)-net in base 4, using

7 times m-reduction [i] based on (48, 102, 65)-net in base 4, using
- base change [i] based on digital (14, 68, 65)-net over F₈, using
  - net from sequence [i] based on digital (14, 64)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65, using
      - the Suzuki function field over F₈ [i]

(48, 48+47, 81)-Net over F₄ — Digital

Digital (48, 95, 81)-net over F₄, using

t-expansion [i] based on digital (46, 95, 81)-net over F₄, using
- net from sequence [i] based on digital (46, 80)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 46 and N(F) ≥ 81, using
    - Drinfeld modules of rank 1 [i]

(48, 48+47, 889)-Net in Base 4 — Upper bound on s

There is no (48, 95, 890)-net in base 4, because

1 times m-reduction [i] would yield (48, 94, 890)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 400 857896 094536 577885 230306 605542 166578 298524 705266 729836 > 4⁹⁴ [i]