MinT - Best Known (157−47, 157, s)-Nets in Base 3

Best Known (157−47, 157, s)-Nets in Base 3

(157−47, 157, 204)-Net over F₃ — Constructive and digital

Digital (110, 157, 204)-net over F₃, using

3¹ times duplication [i] based on digital (109, 156, 204)-net over F₃, using
- trace code for nets [i] based on digital (5, 52, 68)-net over F₂₇, using
  - net from sequence [i] based on digital (5, 67)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 5 and N(F) ≥ 68, using
      - a function field by SÃ©mirat [i]

(157−47, 157, 363)-Net over F₃ — Digital

Digital (110, 157, 363)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(157−47, 157, 8097)-Net in Base 3 — Upper bound on s

There is no (110, 157, 8098)-net in base 3, because

1 times m-reduction [i] would yield (110, 156, 8098)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 270 126487 666741 079541 563671 699997 692774 690526 974232 556038 048727 012295 889481 > 3¹⁵⁶ [i]