MinT - Best Known (147−78, 147, s)-Nets in Base 9

Best Known (147−78, 147, s)-Nets in Base 9

(147−78, 147, 165)-Net over F₉ — Constructive and digital

Digital (69, 147, 165)-net over F₉, using

t-expansion [i] based on digital (64, 147, 165)-net over F₉, using
- net from sequence [i] based on digital (64, 164)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 64 and N(F) ≥ 165, using
    - T₄ from the second tower of function fields by GarcÃa and Stichtenoth over F₉ [i]

(147−78, 147, 212)-Net over F₉ — Digital

Digital (69, 147, 212)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(147−78, 147, 7581)-Net in Base 9 — Upper bound on s

There is no (69, 147, 7582)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 188 665976 308554 315822 500236 994827 334555 990064 846766 794946 835583 176462 651803 191464 277761 894263 194797 661575 617303 504723 123288 323488 433451 894225 > 9¹⁴⁷ [i]