MinT - Best Known (228−103, 228, s)-Nets in Base 4

Best Known (228−103, 228, s)-Nets in Base 4

(228−103, 228, 130)-Net over F₄ — Constructive and digital

Digital (125, 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]

(228−103, 228, 222)-Net over F₄ — Digital

Digital (125, 228, 222)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(228−103, 228, 3124)-Net in Base 4 — Upper bound on s

There is no (125, 228, 3125)-net in base 4, because

1 times m-reduction [i] would yield (125, 227, 3125)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 47218 267038 863801 262108 014336 291317 650455 917354 151807 914055 622074 235253 350660 643957 597002 722650 131824 372693 218569 276069 611059 232393 227876 > 4²²⁷ [i]