MinT - Best Known (142−43, 142, s)-Nets in Base 3

Best Known (142−43, 142, s)-Nets in Base 3

(142−43, 142, 192)-Net over F₃ — Constructive and digital

Digital (99, 142, 192)-net over F₃, using

3¹ times duplication [i] based on digital (98, 141, 192)-net over F₃, using
- trace code for nets [i] based on digital (4, 47, 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]

(142−43, 142, 322)-Net over F₃ — Digital

Digital (99, 142, 322)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(142−43, 142, 6913)-Net in Base 3 — Upper bound on s

There is no (99, 142, 6914)-net in base 3, because

1 times m-reduction [i] would yield (99, 141, 6914)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 18 817889 134856 549217 992111 354464 716948 112351 678190 728785 800019 375741 > 3¹⁴¹ [i]