MinT - Best Known (231−102, 231, s)-Nets in Base 4

Best Known (231−102, 231, s)-Nets in Base 4

(231−102, 231, 130)-Net over F₄ — Constructive and digital

Digital (129, 231, 130)-net over F₄, using

t-expansion [i] based on digital (105, 231, 130)-net over F₄, using
- net from sequence [i] based on digital (105, 129)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 105 and N(F) ≥ 130, using
    - T₇ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(231−102, 231, 241)-Net over F₄ — Digital

Digital (129, 231, 241)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(231−102, 231, 3487)-Net in Base 4 — Upper bound on s

There is no (129, 231, 3488)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 11 963457 216835 654783 767677 110500 157356 107542 319482 952752 709460 890170 032104 386161 754600 264031 145494 854855 991214 919818 488778 290141 143128 518740 > 4²³¹ [i]