MinT - Best Known (177−75, 177, s)-Nets in Base 3

Best Known (177−75, 177, s)-Nets in Base 3

(177−75, 177, 128)-Net over F₃ — Constructive and digital

Digital (102, 177, 128)-net over F₃, using

1 times m-reduction [i] based on digital (102, 178, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 89, 64)-net over F₉, using
  - net from sequence [i] based on digital (13, 63)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
      - a function field by GarcÃa and Quoos [i]

(177−75, 177, 143)-Net over F₃ — Digital

Digital (102, 177, 143)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(177−75, 177, 1326)-Net in Base 3 — Upper bound on s

There is no (102, 177, 1327)-net in base 3, because

1 times m-reduction [i] would yield (102, 176, 1327)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 948141 592459 572683 204505 855989 133976 293000 165134 886679 773104 508967 902872 889769 618071 > 3¹⁷⁶ [i]