MinT - Best Known (127−80, 127, s)-Nets in Base 9

Best Known (127−80, 127, s)-Nets in Base 9

(127−80, 127, 81)-Net over F₉ — Constructive and digital

Digital (47, 127, 81)-net over F₉, using

t-expansion [i] based on digital (32, 127, 81)-net over F₉, using
- net from sequence [i] based on digital (32, 80)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 32 and N(F) ≥ 81, using
    - F₄ from the tower of function fields by Bezerra and GarcÃa over F₉ [i]

(127−80, 127, 162)-Net over F₉ — Digital

Digital (47, 127, 162)-net over F₉, using

t-expansion [i] based on digital (46, 127, 162)-net over F₉, using
- net from sequence [i] based on digital (46, 161)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 46 and N(F) ≥ 162, using
    - a curve from the manYPoints database [i]

(127−80, 127, 2086)-Net in Base 9 — Upper bound on s

There is no (47, 127, 2087)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 15 664408 207986 689392 918346 585869 778069 804510 078575 194372 612734 832856 880336 086384 647476 469198 950273 231254 679886 191203 177665 > 9¹²⁷ [i]