MinT - Best Known (113, 113+136, s)-Nets in Base 3

Best Known (113, 113+136, s)-Nets in Base 3

(113, 113+136, 74)-Net over F₃ — Constructive and digital

Digital (113, 249, 74)-net over F₃, using

t-expansion [i] based on digital (107, 249, 74)-net over F₃, using
- net from sequence [i] based on digital (107, 73)-sequence over F₃, using
  - base reduction for sequences [i] based on digital (17, 73)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
      - a function field by GarcÃa and Quoos [i]

(113, 113+136, 120)-Net over F₃ — Digital

Digital (113, 249, 120)-net over F₃, using

net from sequence [i] based on digital (113, 119)-sequence over F₃, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 113 and N(F) ≥ 120, using
  - algebraic function fields over â„¤₃ by Niederreiter/Xing [i]

(113, 113+136, 665)-Net in Base 3 — Upper bound on s

There is no (113, 249, 666)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 66543 745243 751920 981063 710335 526255 363768 248686 294035 407583 362743 421291 604178 955844 345657 979284 840732 822780 811984 643625 > 3²⁴⁹ [i]