MinT - Best Known (127−37, 127, s)-Nets in Base 3

Best Known (127−37, 127, s)-Nets in Base 3

(127−37, 127, 204)-Net over F₃ — Constructive and digital

Digital (90, 127, 204)-net over F₃, using

3¹ times duplication [i] based on digital (89, 126, 204)-net over F₃, using
- trace code for nets [i] based on digital (5, 42, 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]

(127−37, 127, 336)-Net over F₃ — Digital

Digital (90, 127, 336)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(127−37, 127, 8241)-Net in Base 3 — Upper bound on s

There is no (90, 127, 8242)-net in base 3, because

1 times m-reduction [i] would yield (90, 126, 8242)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1 310243 042804 456383 019050 418297 266343 280160 223307 743371 884885 > 3¹²⁶ [i]