MinT - Best Known (176−75, 176, s)-Nets in Base 3

Best Known (176−75, 176, s)-Nets in Base 3

(176−75, 176, 128)-Net over F₃ — Constructive and digital

Digital (101, 176, 128)-net over F₃, using

trace code for nets [i] based on digital (13, 88, 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]

(176−75, 176, 140)-Net over F₃ — Digital

Digital (101, 176, 140)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(176−75, 176, 1286)-Net in Base 3 — Upper bound on s

There is no (101, 176, 1287)-net in base 3, because

1 times m-reduction [i] would yield (101, 175, 1287)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 314869 210156 072957 001931 719227 479786 929555 248428 028608 249005 899006 573489 060941 011975 > 3¹⁷⁵ [i]