MinT - Best Known (75, 75+66, s)-Nets in Base 9

Best Known (75, 75+66, s)-Nets in Base 9

(75, 75+66, 300)-Net over F₉ — Constructive and digital

Digital (75, 141, 300)-net over F₉, using

1 times m-reduction [i] based on digital (75, 142, 300)-net over F₉, using
- trace code for nets [i] based on digital (4, 71, 150)-net over F₈₁, using
  - net from sequence [i] based on digital (4, 149)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 4 and N(F) ≥ 150, using
      - a function field by SÃ©mirat [i]

(75, 75+66, 349)-Net over F₉ — Digital

Digital (75, 141, 349)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(75, 75+66, 19635)-Net in Base 9 — Upper bound on s

There is no (75, 141, 19636)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 353 761303 044164 784486 869606 218738 312485 642831 765402 822462 253360 153319 084587 119182 987219 931099 398012 340755 010813 367465 703945 950293 107105 > 9¹⁴¹ [i]