MinT - Best Known (91, 91+36, s)-Nets in Base 3

Best Known (91, 91+36, s)-Nets in Base 3

(91, 91+36, 228)-Net over F₃ — Constructive and digital

Digital (91, 127, 228)-net over F₃, using

3¹ times duplication [i] based on digital (90, 126, 228)-net over F₃, using
- trace code for nets [i] based on digital (6, 42, 76)-net over F₂₇, using
  - net from sequence [i] based on digital (6, 75)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 6 and N(F) ≥ 76, using
      - a function field by SÃ©mirat [i]

(91, 91+36, 370)-Net over F₃ — Digital

Digital (91, 127, 370)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(91, 91+36, 8761)-Net in Base 3 — Upper bound on s

There is no (91, 127, 8762)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3 932258 049542 241206 351322 566403 703886 234466 735373 823026 808901 > 3¹²⁷ [i]