MinT - Best Known (255−180, 255, s)-Nets in Base 4

Best Known (255−180, 255, s)-Nets in Base 4

(255−180, 255, 104)-Net over F₄ — Constructive and digital

Digital (75, 255, 104)-net over F₄, using

t-expansion [i] based on digital (73, 255, 104)-net over F₄, using
- net from sequence [i] based on digital (73, 103)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 104, using
    - F₆ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(255−180, 255, 112)-Net over F₄ — Digital

Digital (75, 255, 112)-net over F₄, using

t-expansion [i] based on digital (73, 255, 112)-net over F₄, using
- net from sequence [i] based on digital (73, 111)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 112, using
    - Drinfeld modules of rank 1 [i]

(255−180, 255, 509)-Net in Base 4 — Upper bound on s

There is no (75, 255, 510)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3552 975203 801362 001954 461985 329100 262751 026387 008019 050880 418081 516763 887501 326656 295371 262373 320250 593017 550073 362340 560689 187166 054311 030017 742894 069442 > 4²⁵⁵ [i]