MinT - Best Known (228−101, 228, s)-Nets in Base 4

Best Known (228−101, 228, s)-Nets in Base 4

(228−101, 228, 130)-Net over F₄ — Constructive and digital

Digital (127, 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]

(228−101, 228, 236)-Net over F₄ — Digital

Digital (127, 228, 236)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(228−101, 228, 3473)-Net in Base 4 — Upper bound on s

There is no (127, 228, 3474)-net in base 4, because

1 times m-reduction [i] would yield (127, 227, 3474)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 46682 192331 032345 120396 390726 059061 020808 132971 277162 690596 090924 332019 826264 762461 356108 516649 641846 585280 988997 536867 683576 517960 404000 > 4²²⁷ [i]