MinT - Best Known (75, 75+49, s)-Nets in Base 3

Best Known (75, 75+49, s)-Nets in Base 3

(75, 75+49, 128)-Net over F₃ — Constructive and digital

Digital (75, 124, 128)-net over F₃, using

trace code for nets [i] based on digital (13, 62, 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]

(75, 75+49, 129)-Net over F₃ — Digital

Digital (75, 124, 129)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(75, 75+49, 1343)-Net in Base 3 — Upper bound on s

There is no (75, 124, 1344)-net in base 3, because

1 times m-reduction [i] would yield (75, 123, 1344)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 49316 803985 795528 689337 222323 380686 236600 155439 574106 103809 > 3¹²³ [i]