MinT - Best Known (121, 121+128, s)-Nets in Base 4

Best Known (121, 121+128, s)-Nets in Base 4

(121, 121+128, 130)-Net over F₄ — Constructive and digital

Digital (121, 249, 130)-net over F₄, using

t-expansion [i] based on digital (105, 249, 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]

(121, 121+128, 168)-Net over F₄ — Digital

Digital (121, 249, 168)-net over F₄, using

t-expansion [i] based on digital (115, 249, 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]

(121, 121+128, 1757)-Net in Base 4 — Upper bound on s

There is no (121, 249, 1758)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 846567 057994 085952 971957 696187 386739 932556 866184 091388 707657 762482 462251 989038 849378 786415 154638 910124 786793 555479 114334 966322 822466 818152 929803 333875 > 4²⁴⁹ [i]