MinT - Best Known (163, 163+75, s)-Nets in Base 3

Best Known (163, 163+75, s)-Nets in Base 3

(163, 163+75, 192)-Net over F₃ — Constructive and digital

Digital (163, 238, 192)-net over F₃, using

3¹ times duplication [i] based on digital (162, 237, 192)-net over F₃, using
- trace code for nets [i] based on digital (4, 79, 64)-net over F₂₇, using
  - net from sequence [i] based on digital (4, 63)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 4 and N(F) ≥ 64, using
      - a function field by SÃ©mirat [i]

(163, 163+75, 442)-Net over F₃ — Digital

Digital (163, 238, 442)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(163, 163+75, 8301)-Net in Base 3 — Upper bound on s

There is no (163, 238, 8302)-net in base 3, because

1 times m-reduction [i] would yield (163, 237, 8302)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 120087 609800 056056 250867 508355 169160 308251 235980 293453 647577 914284 331490 189690 426028 137370 819172 868392 571611 632693 > 3²³⁷ [i]