MinT - Best Known (119, 119+103, s)-Nets in Base 3

Best Known (119, 119+103, s)-Nets in Base 3

(119, 119+103, 80)-Net over F₃ — Constructive and digital

Digital (119, 222, 80)-net over F₃, using

trace code for nets [i] based on digital (8, 111, 40)-net over F₉, using
- net from sequence [i] based on digital (8, 39)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 8 and N(F) ≥ 40, using
    - a function field by SÃ©mirat [i]

(119, 119+103, 135)-Net over F₃ — Digital

Digital (119, 222, 135)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(119, 119+103, 1110)-Net in Base 3 — Upper bound on s

There is no (119, 222, 1111)-net in base 3, because

1 times m-reduction [i] would yield (119, 221, 1111)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2889 285392 237259 072457 103770 120500 079985 555551 481521 307371 737164 822525 940830 552912 580612 115685 418912 382203 > 3²²¹ [i]