MinT - Best Known (98, 98+77, s)-Nets in Base 3

Best Known (98, 98+77, s)-Nets in Base 3

(98, 98+77, 80)-Net over F₃ — Constructive and digital

Digital (98, 175, 80)-net over F₃, using

5 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]

(98, 98+77, 128)-Net over F₃ — Digital

Digital (98, 175, 128)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(98, 98+77, 1112)-Net in Base 3 — Upper bound on s

There is no (98, 175, 1113)-net in base 3, because

1 times m-reduction [i] would yield (98, 174, 1113)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 106442 712777 914744 970277 304845 292887 449893 271205 745963 318133 675570 267315 403488 773577 > 3¹⁷⁴ [i]