MinT - Best Known (259−125, 259, s)-Nets in Base 4

Best Known (259−125, 259, s)-Nets in Base 4

(259−125, 259, 130)-Net over F₄ — Constructive and digital

Digital (134, 259, 130)-net over F₄, using

t-expansion [i] based on digital (105, 259, 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]

(259−125, 259, 202)-Net over F₄ — Digital

Digital (134, 259, 202)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(259−125, 259, 2503)-Net in Base 4 — Upper bound on s

There is no (134, 259, 2504)-net in base 4, because

1 times m-reduction [i] would yield (134, 258, 2504)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 218539 925885 091535 040245 663505 343652 877457 689669 923808 875505 126063 716360 902230 433343 202296 053717 623534 475076 320942 052585 861435 813158 758095 371410 014444 900840 > 4²⁵⁸ [i]