MinT - Best Known (116, 116+126, s)-Nets in Base 3

Best Known (116, 116+126, s)-Nets in Base 3

(116, 116+126, 74)-Net over F₃ — Constructive and digital

Digital (116, 242, 74)-net over F₃, using

t-expansion [i] based on digital (107, 242, 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]

(116, 116+126, 120)-Net over F₃ — Digital

Digital (116, 242, 120)-net over F₃, using

t-expansion [i] based on digital (113, 242, 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]

(116, 116+126, 766)-Net in Base 3 — Upper bound on s

There is no (116, 242, 767)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 30 954014 243702 420042 028767 363565 903176 188366 850307 510288 024008 884608 339276 652004 982411 248192 280451 052420 056161 840003 > 3²⁴² [i]