MinT - Best Known (180, 180+56, s)-Nets in Base 4

Best Known (180, 180+56, s)-Nets in Base 4

(180, 180+56, 1040)-Net over F₄ — Constructive and digital

Digital (180, 236, 1040)-net over F₄, using

trace code for nets [i] based on digital (3, 59, 260)-net over F₂₅₆, using
- net from sequence [i] based on digital (3, 259)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(180, 180+56, 2753)-Net over F₄ — Digital

Digital (180, 236, 2753)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(180, 180+56, 447061)-Net in Base 4 — Upper bound on s

There is no (180, 236, 447062)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 12194 739943 239057 237970 730191 465556 128266 268904 407302 051189 418431 795800 197280 349602 187034 792444 593255 983811 281957 248677 733790 408843 165674 135480 > 4²³⁶ [i]