MinT - Best Known (83, 83+65, s)-Nets in Base 3

Best Known (83, 83+65, s)-Nets in Base 3

(83, 83+65, 80)-Net over F₃ — Constructive and digital

Digital (83, 148, 80)-net over F₃, using

2 times m-reduction [i] based on digital (83, 150, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 75, 40)-net over F₉, using
  - net from sequence [i] based on digital (8, 39)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 8 and N(F) ≥ 40, using
      - a function field by SÃ©mirat [i]

(83, 83+65, 111)-Net over F₃ — Digital

Digital (83, 148, 111)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(83, 83+65, 963)-Net in Base 3 — Upper bound on s

There is no (83, 148, 964)-net in base 3, because

1 times m-reduction [i] would yield (83, 147, 964)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 13944 159681 175681 195415 112760 565784 167984 905919 383079 776058 801110 396161 > 3¹⁴⁷ [i]