MinT - Best Known (241−134, 241, s)-Nets in Base 3

Best Known (241−134, 241, s)-Nets in Base 3

(241−134, 241, 74)-Net over F₃ — Constructive and digital

Digital (107, 241, 74)-net over F₃, using

net from sequence [i] based on digital (107, 73)-sequence over F₃, using
- base reduction for sequences [i] based on digital (17, 73)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
    - a function field by GarcÃa and Quoos [i]

(241−134, 241, 104)-Net over F₃ — Digital

Digital (107, 241, 104)-net over F₃, using

t-expansion [i] based on digital (102, 241, 104)-net over F₃, using
- net from sequence [i] based on digital (102, 103)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 102 and N(F) ≥ 104, using
    - algebraic function fields over â„¤₃ by Niederreiter/Xing [i]

(241−134, 241, 606)-Net in Base 3 — Upper bound on s

There is no (107, 241, 607)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 9 838231 131699 678346 421309 044191 816082 860669 036503 141701 518536 448022 751428 791463 097304 492342 175313 753666 922058 739451 > 3²⁴¹ [i]