MinT - Best Known (47, 92, s)-Nets in Base 4

Best Known (47, 92, s)-Nets in Base 4

(47, 92, 60)-Net over F₄ — Constructive and digital

Digital (47, 92, 60)-net over F₄, using

(u,Â u+v)-construction [i] based on
1. digital (10, 32, 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, 60, 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]

(47, 92, 65)-Net in Base 4 — Constructive

(47, 92, 65)-net in base 4, using

7 times m-reduction [i] based on (47, 99, 65)-net in base 4, using
- base change [i] based on digital (14, 66, 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]

(47, 92, 81)-Net over F₄ — Digital

Digital (47, 92, 81)-net over F₄, using

t-expansion [i] based on digital (46, 92, 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]

(47, 92, 915)-Net in Base 4 — Upper bound on s

There is no (47, 92, 916)-net in base 4, because

1 times m-reduction [i] would yield (47, 91, 916)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 6 172977 850809 821089 024717 627443 082104 437084 946143 161504 > 4⁹¹ [i]