MinT - Best Known (214−67, 214, s)-Nets in Base 3

Best Known (214−67, 214, s)-Nets in Base 3

(214−67, 214, 192)-Net over F₃ — Constructive and digital

Digital (147, 214, 192)-net over F₃, using

3¹ times duplication [i] based on digital (146, 213, 192)-net over F₃, using
- trace code for nets [i] based on digital (4, 71, 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]

(214−67, 214, 411)-Net over F₃ — Digital

Digital (147, 214, 411)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(214−67, 214, 7872)-Net in Base 3 — Upper bound on s

There is no (147, 214, 7873)-net in base 3, because

1 times m-reduction [i] would yield (147, 213, 7873)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 423517 654260 013186 750717 142595 008776 444761 845105 453092 637591 804613 087578 270507 049172 320526 760483 735811 > 3²¹³ [i]