MinT - Best Known (163, 163+71, s)-Nets in Base 3

Best Known (163, 163+71, s)-Nets in Base 3

(163, 163+71, 246)-Net over F₃ — Constructive and digital

Digital (163, 234, 246)-net over F₃, using

trace code for nets [i] based on digital (7, 78, 82)-net over F₂₇, using
- net from sequence [i] based on digital (7, 81)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 7 and N(F) ≥ 82, using
    - a function field by SÃ©mirat [i]

(163, 163+71, 491)-Net over F₃ — Digital

Digital (163, 234, 491)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(163, 163+71, 10400)-Net in Base 3 — Upper bound on s

There is no (163, 234, 10401)-net in base 3, because

1 times m-reduction [i] would yield (163, 233, 10401)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1478 128218 971575 416804 422676 170582 326525 646036 409362 089314 884800 259274 676070 155329 319213 515845 891193 874532 867355 > 3²³³ [i]