MinT - Best Known (230−79, 230, s)-Nets in Base 3

Best Known (230−79, 230, s)-Nets in Base 3

(230−79, 230, 162)-Net over F₃ — Constructive and digital

Digital (151, 230, 162)-net over F₃, using

8 times m-reduction [i] based on digital (151, 238, 162)-net over F₃, using
- trace code for nets [i] based on digital (32, 119, 81)-net over F₉, using
  - net from sequence [i] based on digital (32, 80)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 32 and N(F) ≥ 81, using
      - F₄ from the tower of function fields by Bezerra and GarcÃa over F₉ [i]

(230−79, 230, 328)-Net over F₃ — Digital

Digital (151, 230, 328)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(230−79, 230, 4836)-Net in Base 3 — Upper bound on s

There is no (151, 230, 4837)-net in base 3, because

1 times m-reduction [i] would yield (151, 229, 4837)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 18 318624 997092 913026 989644 336887 508252 045745 289425 043427 528312 085588 471166 953491 836053 309003 312780 659079 676891 > 3²²⁹ [i]