MinT - Best Known (258−95, 258, s)-Nets in Base 4

Best Known (258−95, 258, s)-Nets in Base 4

(258−95, 258, 200)-Net over F₄ — Constructive and digital

Digital (163, 258, 200)-net over F₄, using

t-expansion [i] based on digital (161, 258, 200)-net over F₄, using
- net from sequence [i] based on digital (161, 199)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 161 and N(F) ≥ 200, using
    - F₇ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(258−95, 258, 484)-Net over F₄ — Digital

Digital (163, 258, 484)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(258−95, 258, 11958)-Net in Base 4 — Upper bound on s

There is no (163, 258, 11959)-net in base 4, because

1 times m-reduction [i] would yield (163, 257, 11959)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 53641 337306 859488 441447 319912 514218 953612 884009 800480 729877 394181 318878 994168 648009 586459 608275 754983 155903 681332 518915 464509 359741 138537 304089 015460 678040 > 4²⁵⁷ [i]