MinT - Best Known (88, 88+35, s)-Nets in Base 3

Best Known (88, 88+35, s)-Nets in Base 3

(88, 88+35, 228)-Net over F₃ — Constructive and digital

Digital (88, 123, 228)-net over F₃, using

trace code for nets [i] based on digital (6, 41, 76)-net over F₂₇, using
- net from sequence [i] based on digital (6, 75)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 6 and N(F) ≥ 76, using
    - a function field by SÃ©mirat [i]

(88, 88+35, 356)-Net over F₃ — Digital

Digital (88, 123, 356)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(88, 88+35, 9510)-Net in Base 3 — Upper bound on s

There is no (88, 123, 9511)-net in base 3, because

1 times m-reduction [i] would yield (88, 122, 9511)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 16183 573486 814550 087746 889364 509615 682972 790231 226690 967599 > 3¹²² [i]