MinT - Best Known (93−48, 93, s)-Nets in Base 4

Best Known (93−48, 93, s)-Nets in Base 4

(93−48, 93, 56)-Net over F₄ — Constructive and digital

Digital (45, 93, 56)-net over F₄, using

t-expansion [i] based on digital (33, 93, 56)-net over F₄, using
- net from sequence [i] based on digital (33, 55)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 33 and N(F) ≥ 56, using
    - F₅ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(93−48, 93, 65)-Net in Base 4 — Constructive

(45, 93, 65)-net in base 4, using

base change [i] based on digital (14, 62, 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]

(93−48, 93, 80)-Net over F₄ — Digital

Digital (45, 93, 80)-net over F₄, using

net from sequence [i] based on digital (45, 79)-sequence over F₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 45 and N(F) ≥ 80, using
  - Drinfeld modules of rank 1 [i]

(93−48, 93, 684)-Net in Base 4 — Upper bound on s

There is no (45, 93, 685)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 100 997685 784719 051797 813256 380729 454276 664065 817742 240494 > 4⁹³ [i]