MinT - Best Known (255−129, 255, s)-Nets in Base 4

Best Known (255−129, 255, s)-Nets in Base 4

(255−129, 255, 130)-Net over F₄ — Constructive and digital

Digital (126, 255, 130)-net over F₄, using

t-expansion [i] based on digital (105, 255, 130)-net over F₄, using
- net from sequence [i] based on digital (105, 129)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 105 and N(F) ≥ 130, using
    - T₇ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(255−129, 255, 176)-Net over F₄ — Digital

Digital (126, 255, 176)-net over F₄, using

t-expansion [i] based on digital (125, 255, 176)-net over F₄, using
- net from sequence [i] based on digital (125, 175)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 125 and N(F) ≥ 176, using
    - Drinfeld modules of rank 1 [i]

(255−129, 255, 1963)-Net in Base 4 — Upper bound on s

There is no (126, 255, 1964)-net in base 4, because

1 times m-reduction [i] would yield (126, 254, 1964)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 839 527333 436448 225603 214172 890407 616232 682397 038730 777290 744021 464860 655136 391320 893557 459390 154546 436200 293888 193432 506256 419516 680600 164204 946637 941550 > 4²⁵⁴ [i]