MinT - Best Known (99, 99+71, s)-Nets in Base 3

Best Known (99, 99+71, s)-Nets in Base 3

(99, 99+71, 128)-Net over F₃ — Constructive and digital

Digital (99, 170, 128)-net over F₃, using

2 times m-reduction [i] based on digital (99, 172, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 86, 64)-net over F₉, using
  - net from sequence [i] 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]

(99, 99+71, 144)-Net over F₃ — Digital

Digital (99, 170, 144)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(99, 99+71, 1365)-Net in Base 3 — Upper bound on s

There is no (99, 170, 1366)-net in base 3, because

1 times m-reduction [i] would yield (99, 169, 1366)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 434 434442 912282 767118 306540 408781 712800 222969 529343 934898 863042 498031 687704 500577 > 3¹⁶⁹ [i]