MinT - Best Known (70, 70+64, s)-Nets in Base 9

Best Known (70, 70+64, s)-Nets in Base 9

(70, 70+64, 232)-Net over F₉ — Constructive and digital

Digital (70, 134, 232)-net over F₉, using

2 times m-reduction [i] based on digital (70, 136, 232)-net over F₉, using
- trace code for nets [i] based on digital (2, 68, 116)-net over F₈₁, using
  - net from sequence [i] based on digital (2, 115)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 116, using
      - a function field by SÃ©mirat [i]

(70, 70+64, 307)-Net over F₉ — Digital

Digital (70, 134, 307)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(70, 70+64, 15817)-Net in Base 9 — Upper bound on s

There is no (70, 134, 15818)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 73 904980 360794 095681 212938 238887 856824 548573 741004 897309 818981 046931 592340 061890 489558 125640 279936 624827 213089 703130 514347 421185 > 9¹³⁴ [i]