MinT - Best Known (228−107, 228, s)-Nets in Base 4

Best Known (228−107, 228, s)-Nets in Base 4

(228−107, 228, 130)-Net over F₄ — Constructive and digital

Digital (121, 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]

(228−107, 228, 197)-Net over F₄ — Digital

Digital (121, 228, 197)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(228−107, 228, 2558)-Net in Base 4 — Upper bound on s

There is no (121, 228, 2559)-net in base 4, because

1 times m-reduction [i] would yield (121, 227, 2559)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 46906 025944 381563 055828 677397 113463 345047 853335 518011 351860 799151 268786 487281 064343 880235 802951 653963 253523 747191 567071 475071 650024 563266 > 4²²⁷ [i]