MinT - Best Known (122, 122+129, s)-Nets in Base 4

Best Known (122, 122+129, s)-Nets in Base 4

(122, 122+129, 130)-Net over F₄ — Constructive and digital

Digital (122, 251, 130)-net over F₄, using

t-expansion [i] based on digital (105, 251, 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]

(122, 122+129, 168)-Net over F₄ — Digital

Digital (122, 251, 168)-net over F₄, using

t-expansion [i] based on digital (115, 251, 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]

(122, 122+129, 1796)-Net in Base 4 — Upper bound on s

There is no (122, 251, 1797)-net in base 4, because

1 times m-reduction [i] would yield (122, 250, 1797)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3 313553 717605 653818 771616 903413 494681 227667 090983 763108 811910 707788 323743 902001 223282 765616 387195 320058 159642 469874 818646 746126 847629 554021 465163 676100 > 4²⁵⁰ [i]