MinT - Best Known (148, 148+48, s)-Nets in Base 3

Best Known (148, 148+48, s)-Nets in Base 3

(148, 148+48, 400)-Net over F₃ — Constructive and digital

Digital (148, 196, 400)-net over F₃, using

trace code for nets [i] based on digital (1, 49, 100)-net over F₈₁, using
- net from sequence [i] based on digital (1, 99)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 1 and N(F) ≥ 100, using
    - a function field by SÃ©mirat [i]

(148, 148+48, 908)-Net over F₃ — Digital

Digital (148, 196, 908)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(148, 148+48, 38597)-Net in Base 3 — Upper bound on s

There is no (148, 196, 38598)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3280 287454 197902 373748 505256 763198 174497 009691 975582 082233 295236 507416 442935 439754 761505 499249 > 3¹⁹⁶ [i]