MinT - Best Known (242−65, 242, s)-Nets in Base 3

Best Known (242−65, 242, s)-Nets in Base 3

(242−65, 242, 288)-Net over F₃ — Constructive and digital

Digital (177, 242, 288)-net over F₃, using

7 times m-reduction [i] based on digital (177, 249, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 83, 96)-net over F₂₇, using
  - net from sequence [i] based on digital (11, 95)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 11 and N(F) ≥ 96, using
      - an explicitly constructive algebraic function field [i]

(242−65, 242, 761)-Net over F₃ — Digital

Digital (177, 242, 761)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(242−65, 242, 25039)-Net in Base 3 — Upper bound on s

There is no (177, 242, 25040)-net in base 3, because

1 times m-reduction [i] would yield (177, 241, 25040)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 9 695029 449325 649060 041000 195915 963410 329286 250536 582400 100974 805163 339893 201214 161796 286439 631142 937454 195596 908545 > 3²⁴¹ [i]