MinT - Best Known (238−133, 238, s)-Nets in Base 4

Best Known (238−133, 238, s)-Nets in Base 4

(238−133, 238, 130)-Net over F₄ — Constructive and digital

Digital (105, 238, 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]

(238−133, 238, 144)-Net over F₄ — Digital

Digital (105, 238, 144)-net over F₄, using

t-expansion [i] based on digital (91, 238, 144)-net over F₄, using
- net from sequence [i] based on digital (91, 143)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 91 and N(F) ≥ 144, using
    - Drinfeld modules of rank 1 [i]

(238−133, 238, 1176)-Net in Base 4 — Upper bound on s

There is no (105, 238, 1177)-net in base 4, because

1 times m-reduction [i] would yield (105, 237, 1177)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 50330 235798 866884 126217 615613 801969 173661 358895 828589 053031 084359 741118 949715 674425 976150 549601 977596 056020 086658 170537 054562 123923 093126 206584 > 4²³⁷ [i]