MinT - Best Known (79, 79+112, s)-Nets in Base 3

Best Known (79, 79+112, s)-Nets in Base 3

(79, 79+112, 54)-Net over F₃ — Constructive and digital

Digital (79, 191, 54)-net over F₃, using

net from sequence [i] based on digital (79, 53)-sequence over F₃, using
- base reduction for sequences [i] based on digital (13, 53)-sequence over F₉, using
  - s-reduction based on digital (13, 63)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
      - a function field by GarcÃa and Quoos [i]

(79, 79+112, 84)-Net over F₃ — Digital

Digital (79, 191, 84)-net over F₃, using

t-expansion [i] based on digital (71, 191, 84)-net over F₃, using
- net from sequence [i] based on digital (71, 83)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 71 and N(F) ≥ 84, using
    - algebraic function fields over â„¤₃ by Niederreiter/Xing [i]

(79, 79+112, 407)-Net in Base 3 — Upper bound on s

There is no (79, 191, 408)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 14 690364 869983 073818 751659 005998 521503 147588 977692 260562 000023 737440 561495 356468 442454 975745 > 3¹⁹¹ [i]