MinT - Best Known (99, 99+95, s)-Nets in Base 3

Best Known (99, 99+95, s)-Nets in Base 3

(99, 99+95, 72)-Net over F₃ — Constructive and digital

Digital (99, 194, 72)-net over F₃, using

(u,Â u+v)-construction [i] based on
1. digital (26, 73, 36)-net over F₃, using
  - net from sequence [i] based on digital (26, 35)-sequence over F₃, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 26 and N(F) ≥ 36, using
      - an explicitly constructive algebraic function field [i]
2. digital (26, 121, 36)-net over F₃, using
  - net from sequence [i] based on digital (26, 35)-sequence over F₃ (see above)

(99, 99+95, 103)-Net over F₃ — Digital

Digital (99, 194, 103)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(99, 99+95, 790)-Net in Base 3 — Upper bound on s

There is no (99, 194, 791)-net in base 3, because

1 times m-reduction [i] would yield (99, 193, 791)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 123 171999 854162 349807 662178 180768 924222 370043 592673 327453 144946 618732 264993 376436 350964 050435 > 3¹⁹³ [i]