MinT - Best Known (228−113, 228, s)-Nets in Base 4

Best Known (228−113, 228, s)-Nets in Base 4

(228−113, 228, 130)-Net over F₄ — Constructive and digital

Digital (115, 228, 130)-net over F₄, using

t-expansion [i] based on digital (105, 228, 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]

(228−113, 228, 168)-Net over F₄ — Digital

Digital (115, 228, 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]

(228−113, 228, 1949)-Net in Base 4 — Upper bound on s

There is no (115, 228, 1950)-net in base 4, because

1 times m-reduction [i] would yield (115, 227, 1950)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 47100 709138 568263 103808 111117 080900 981131 141224 977946 087510 387938 027175 874181 868868 007150 439188 180229 078921 391177 361327 528160 041444 555908 > 4²²⁷ [i]