MinT - Best Known (243−85, 243, s)-Nets in Base 3

Best Known (243−85, 243, s)-Nets in Base 3

(243−85, 243, 162)-Net over F₃ — Constructive and digital

Digital (158, 243, 162)-net over F₃, using

t-expansion [i] based on digital (157, 243, 162)-net over F₃, using
- 7 times m-reduction [i] based on digital (157, 250, 162)-net over F₃, using
  - trace code for nets [i] based on digital (32, 125, 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]

(243−85, 243, 326)-Net over F₃ — Digital

Digital (158, 243, 326)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(243−85, 243, 4592)-Net in Base 3 — Upper bound on s

There is no (158, 243, 4593)-net in base 3, because

1 times m-reduction [i] would yield (158, 242, 4593)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 29 315354 890318 933070 710770 937199 085129 214995 142874 001082 629755 537124 927217 326518 295294 010003 673437 510255 904971 894665 > 3²⁴² [i]