MinT - Best Known (255−126, 255, s)-Nets in Base 4

Best Known (255−126, 255, s)-Nets in Base 4

(255−126, 255, 130)-Net over F₄ — Constructive and digital

Digital (129, 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]

(255−126, 255, 185)-Net over F₄ — Digital

Digital (129, 255, 185)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(255−126, 255, 2163)-Net in Base 4 — Upper bound on s

There is no (129, 255, 2164)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3362 094592 733863 289161 050187 577428 362490 474291 725433 150923 640304 674923 858444 113265 144611 585665 984429 534077 212701 569834 195260 029610 447651 804686 942396 957840 > 4²⁵⁵ [i]