MinT - Best Known (148−72, 148, s)-Nets in Base 9

Best Known (148−72, 148, s)-Nets in Base 9

(148−72, 148, 232)-Net over F₉ — Constructive and digital

Digital (76, 148, 232)-net over F₉, using

trace code for nets [i] based on digital (2, 74, 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]

(148−72, 148, 308)-Net over F₉ — Digital

Digital (76, 148, 308)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(148−72, 148, 14928)-Net in Base 9 — Upper bound on s

There is no (76, 148, 14929)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 1693 647835 446091 293783 069136 726114 538127 149787 705858 356802 958832 326046 379201 762165 458031 644557 591398 744252 879404 708419 402204 521160 600207 074465 > 9¹⁴⁸ [i]