MinT - Best Known (75−36, 75, s)-Nets in Base 4

Best Known (75−36, 75, s)-Nets in Base 4

(75−36, 75, 56)-Net over F₄ — Constructive and digital

Digital (39, 75, 56)-net over F₄, using

t-expansion [i] based on digital (33, 75, 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]

(75−36, 75, 65)-Net in Base 4 — Constructive

(39, 75, 65)-net in base 4, using

base change [i] based on digital (14, 50, 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]

(75−36, 75, 73)-Net over F₄ — Digital

Digital (39, 75, 73)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(75−36, 75, 797)-Net in Base 4 — Upper bound on s

There is no (39, 75, 798)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1437 825290 190030 008691 444778 665605 607444 009970 > 4⁷⁵ [i]