MinT - Best Known (258−134, 258, s)-Nets in Base 4

Best Known (258−134, 258, s)-Nets in Base 4

(258−134, 258, 130)-Net over F₄ — Constructive and digital

Digital (124, 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]

(258−134, 258, 168)-Net over F₄ — Digital

Digital (124, 258, 168)-net over F₄, using

t-expansion [i] based on digital (115, 258, 168)-net over F₄, using
- net from sequence [i] based on digital (115, 167)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 115 and N(F) ≥ 168, using
    - Drinfeld modules of rank 1 [i]

(258−134, 258, 1734)-Net in Base 4 — Upper bound on s

There is no (124, 258, 1735)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 219430 559585 056917 960874 916471 885272 651353 118654 593433 261946 424359 922798 801153 460315 578792 914404 156483 577331 803361 300790 634649 038520 002544 734321 580291 601648 > 4²⁵⁸ [i]