MinT - Best Known (98, 98+41, s)-Nets in Base 3

Best Known (98, 98+41, s)-Nets in Base 3

(98, 98+41, 204)-Net over F₃ — Constructive and digital

Digital (98, 139, 204)-net over F₃, using

3¹ times duplication [i] based on digital (97, 138, 204)-net over F₃, using
- trace code for nets [i] based on digital (5, 46, 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]

(98, 98+41, 345)-Net over F₃ — Digital

Digital (98, 139, 345)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(98, 98+41, 8116)-Net in Base 3 — Upper bound on s

There is no (98, 139, 8117)-net in base 3, because

1 times m-reduction [i] would yield (98, 138, 8117)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 696958 665043 280338 207315 137660 779328 433067 647680 996084 550425 145233 > 3¹³⁸ [i]