MinT - Best Known (132−53, 132, s)-Nets in Base 3

Best Known (132−53, 132, s)-Nets in Base 3

(132−53, 132, 128)-Net over F₃ — Constructive and digital

Digital (79, 132, 128)-net over F₃, using

trace code for nets [i] based on digital (13, 66, 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]

(132−53, 132, 130)-Net over F₃ — Digital

Digital (79, 132, 130)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(132−53, 132, 1311)-Net in Base 3 — Upper bound on s

There is no (79, 132, 1312)-net in base 3, because

1 times m-reduction [i] would yield (79, 131, 1312)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 318 493832 086374 036894 857072 162685 825151 883919 194320 095606 828225 > 3¹³¹ [i]