MinT - Best Known (258−130, 258, s)-Nets in Base 4

Best Known (258−130, 258, s)-Nets in Base 4

(258−130, 258, 130)-Net over F₄ — Constructive and digital

Digital (128, 258, 130)-net over F₄, using

t-expansion [i] based on digital (105, 258, 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]

(258−130, 258, 176)-Net over F₄ — Digital

Digital (128, 258, 176)-net over F₄, using

t-expansion [i] based on digital (125, 258, 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]

(258−130, 258, 1994)-Net in Base 4 — Upper bound on s

There is no (128, 258, 1995)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 216214 653811 768437 803092 906826 740345 861483 088362 852650 371246 574509 612103 135553 474958 967397 811549 166324 165499 676160 965186 645315 967083 674605 009325 205001 664822 > 4²⁵⁸ [i]