MinT - Best Known (178−80, 178, s)-Nets in Base 3

Best Known (178−80, 178, s)-Nets in Base 3

(178−80, 178, 80)-Net over F₃ — Constructive and digital

Digital (98, 178, 80)-net over F₃, using

2 times m-reduction [i] based on digital (98, 180, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 90, 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]

(178−80, 178, 122)-Net over F₃ — Digital

Digital (98, 178, 122)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(178−80, 178, 1008)-Net in Base 3 — Upper bound on s

There is no (98, 178, 1009)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 8 753908 937255 827007 547931 527598 198811 169404 252378 154771 810647 749457 086985 990268 456993 > 3¹⁷⁸ [i]