MinT - Best Known (207−65, 207, s)-Nets in Base 3

Best Known (207−65, 207, s)-Nets in Base 3

(207−65, 207, 192)-Net over F₃ — Constructive and digital

Digital (142, 207, 192)-net over F₃, using

trace code for nets [i] based on digital (4, 69, 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]

(207−65, 207, 396)-Net over F₃ — Digital

Digital (142, 207, 396)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(207−65, 207, 7507)-Net in Base 3 — Upper bound on s

There is no (142, 207, 7508)-net in base 3, because

1 times m-reduction [i] would yield (142, 206, 7508)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 193 931538 101523 349120 319337 628615 550226 024744 545686 610510 887285 340428 204919 931402 643396 741106 941185 > 3²⁰⁶ [i]