MinT - Best Known (102−44, 102, s)-Nets in Base 9

Best Known (102−44, 102, s)-Nets in Base 9

(102−44, 102, 344)-Net over F₉ — Constructive and digital

Digital (58, 102, 344)-net over F₉, using

trace code for nets [i] based on digital (7, 51, 172)-net over F₈₁, using
- net from sequence [i] based on digital (7, 171)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 7 and N(F) ≥ 172, using
    - a function field by SÃ©mirat [i]

(102−44, 102, 386)-Net over F₉ — Digital

Digital (58, 102, 386)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(102−44, 102, 30046)-Net in Base 9 — Upper bound on s

There is no (58, 102, 30047)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 21 530271 388856 761355 147079 363341 419530 583223 189106 819862 446526 359709 247500 955343 167141 300819 524945 > 9¹⁰² [i]