MinT - Best Known (242−57, 242, s)-Nets in Base 3

Best Known (242−57, 242, s)-Nets in Base 3

(242−57, 242, 464)-Net over F₃ — Constructive and digital

Digital (185, 242, 464)-net over F₃, using

2 times m-reduction [i] based on digital (185, 244, 464)-net over F₃, using
- trace code for nets [i] based on digital (2, 61, 116)-net over F₈₁, using
  - net from sequence [i] based on digital (2, 115)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 116, using
      - a function field by SÃ©mirat [i]

(242−57, 242, 1266)-Net over F₃ — Digital

Digital (185, 242, 1266)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(242−57, 242, 72187)-Net in Base 3 — Upper bound on s

There is no (185, 242, 72188)-net in base 3, because

1 times m-reduction [i] would yield (185, 241, 72188)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 9 690588 454793 015248 688774 039304 662371 548032 528206 200816 081326 118638 228638 507534 710070 486194 866082 421639 107647 658177 > 3²⁴¹ [i]