MinT - Best Known (122, 122+131, s)-Nets in Base 4

Best Known (122, 122+131, s)-Nets in Base 4

(122, 122+131, 130)-Net over F₄ — Constructive and digital

Digital (122, 253, 130)-net over F₄, using

t-expansion [i] based on digital (105, 253, 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+131, 168)-Net over F₄ — Digital

Digital (122, 253, 168)-net over F₄, using

t-expansion [i] based on digital (115, 253, 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+131, 1748)-Net in Base 4 — Upper bound on s

There is no (122, 253, 1749)-net in base 4, because

1 times m-reduction [i] would yield (122, 252, 1749)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 52 679489 049038 975196 770798 482503 350275 765119 485270 077943 891598 654323 668148 066658 769461 516257 408830 920378 949760 023812 639706 953486 069034 961738 174068 292416 > 4²⁵² [i]